The father of a murdered New Jersey family was threatened for making anti-Muslim remarks online – and the gruesome quadruple slaying may have been the hateful retaliation, sources told The Post yesterday.

Hossam Armanious, 47, who along with his wife and two daughters was found stabbed to death in his Jersey City home early Friday, would regularly debate religion in a Middle Eastern chat room, one source said.

Armanious, an Egyptian Christian, was well known for expressing his Coptic beliefs and engaging in fiery back-and-forth with Muslims on the Web site paltalk.com.

He “had the reputation for being one of the most outspoken Egyptian Christians,” said the source, who had close ties to the family.

The source, who had knowledge of the investigation, refused to specify the anti-Muslim statement. But he said cops told him they were looking into the exchanges as a possible motive.

“There are several theories we are looking into,” said Assistant Prosecutor Guy Gregory. “But we are not commenting on any of them at this time,” adding that they have discounted the theory of a dispute with a prior tenant of the house lead to the slaugther.

The married father of two had recently been threatened by Muslim members of the Web site, said a fellow Copt and store clerk who uses the chat room.

“You’d better stop this bull—- or we are going to track you down like a chicken and kill you,” was the threat, said the clerk, who was online at the time and saw the exchange.

But Armanious refused to back down, according to two sources who use the Web site. But a relative of the mayor who answered the phone at Healy’s home said there was information the murders were “religion-related.”

Armanious’ fervor apparently rubbed off on his daughter, Sylvia – who would have turned 16 yesterday.

“She was very religious and very opinionated,” said Jessica Cimino, 15, a fellow sophomore at Dickenson HS.

A family member who viewed photos of the bloodbath said Sylvia seemed to have taken the most savage punishment.

“When we saw the pictures, you could tell that they were hurt really, really bad in the face; especially Sylvia,” said Milad Garas, the high-school sophomore’s great-uncle.

The heartless killer not only slit Sylvia’s throat, but also sliced a huge gash in her chest and stabbed her in the wrist, where the young girl had a tattoo of an Egyptian Christian cross.

Also found murdered were the wife, Amal Garas, and the parents’ other daughter, Monica.

Fred Ayed, the deacon at St. George and St. Shenouda church, where the deeply religious family attended services, said he’s worried that the murders could have a ripple effect.

“I am concerned for the safety of our community,” said Ayed, who knew Hossam for 30 years.

“People are scared because one family was slain like cows,” said Moheb Ghabour, publisher of a local newspaper for the Coptic community.

Osama Hassan, director of the Islamic Center of Jersey City, described the relationship between Copts and Muslims as cooperative if not friendly.

“I think there might be people that can get into physical fights, but not to the point of murder,” Hassan said.

Both the deacon and uncle poured cold water on the theory that the family were the victims of a robbery gone wrong.

“This is not a robbery, Ayed said. “We found all of the jewelry in the house. They didn’t take anything.”

The FBI has been called in to help with the case.

“We’re assisting at the request of the Hudson County Prosecutor’s Office and the Jersey City Police Department,” FBI spokesman Stephen Kodak said.